Subgroups — #26106879

Order 12032.

718 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13093986	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#20243133	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15688852	C₂	1	1	yes	maximal, characteristic
5	C₂×#15688850	C₂	1	1	yes	maximal, characteristic
6	#20241229	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×#13093986	C₄	1	2	yes	—
10	C₂×C₄²×D₄₇	—	2	1	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₈×Dic₄₇	—	2	1	no	—
14	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
15	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
16	#15688970	—	2	2	no	—
17	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
18	#15688877	—	2	1	no	—
19	#15688877	—	2	2	no	—
20	#15688852	C₄	1	4	yes	complemented
21	#15688850	C₄	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×D₄₇	—	2	1	no	—
27	C₂²×C₄×D₄₇	—	2	2	no	—
28	C₂²×C₄₇⋊C₈	—	2	1	no	—
29	C₂²×C₄₇⋊C₈	—	2	1	no	—
30	C₄×D₁₈₈	—	2	1	no	—
31	C₄×D₁₈₈	—	2	1	no	—
32	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
33	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
34	#13093986	—	2	4	no	—
35	#13093986	C₈	1	8	yes	complemented
36	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
38	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
39	C₂×C₄×Dic₄₇	—	2	2	no	—
40	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
41	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
42	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
43	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
44	C₄²×D₄₇	—	4	2	no	—
45	C₄²×D₄₇	—	4	2	no	—
46	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
47	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	complemented
48	C₄×C₄₇⋊C₈	—	2	1	no	—
49	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	complemented
50	C₈×Dic₄₇	—	4	2	no	—
51	C₄₇⋊#95	—	2	2	no	—
52	C₂²×C₈×C₄₇	—	2	1	no	—
53	C₂²×C₈×C₄₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₄₇	—	2	1	no	—
56	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
57	C₄⋊C₈×C₄₇	—	2	1	no	—
58	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	complemented
59	C₄×C₈×C₄₇	—	2	1	no	—
60	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	complemented
61	#95×C₄₇	—	2	1	no	—
62	C₂³×D₄₇	—	2	1	no	—
63	C₂²×C₄×C₄₇	—	2	2	no	—
64	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
67	C₂²×Dic₄₇	—	2	1	no	—
68	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
69	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
70	C₂×D₁₈₈	—	2	1	no	—
71	C₂×D₁₈₈	—	2	2	no	—
72	C₂×D₁₈₈	C₄²	1	2	yes	—
73	C₂×D₁₈₈	C₂×C₈	1	4	yes	—
74	C₂×C₄×D₄₇	—	2	2	no	—
75	C₂×C₄×D₄₇	—	2	2	no	—
76	C₂×C₄×D₄₇	—	2	8	no	—
77	C₂×C₄×D₄₇	—	4	4	no	—
78	C₂×C₄×D₄₇	—	4	4	no	—
79	C₂×C₄×D₄₇	—	4	1	no	—
80	C₂×C₄×D₄₇	—	4	1	no	—
81	C₂×C₄×D₄₇	—	4	1	no	—
82	C₂×C₄×D₄₇	—	4	1	no	—
83	C₂×C₈×C₄₇	—	2	2	no	—
84	C₂×C₈×C₄₇	—	2	2	no	—
85	C₂×C₈×C₄₇	—	4	2	no	—
86	C₂×C₈×C₄₇	—	4	1	no	—
87	C₂×C₈×C₄₇	—	4	1	no	—
88	C₄⋊C₄×C₄₇	—	2	2	no	—
89	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	—
90	C₄²×C₄₇	—	4	1	no	—
91	C₄²×C₄₇	—	4	1	no	—
92	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₄²×C₄₇	#41	1	1	yes	characteristic
95	C₄²×C₄₇	#41	1	1	yes	characteristic
96	(C₂×D₄₇)⋊C₄	—	2	2	no	—
97	(C₂×D₄₇)⋊C₄	—	2	2	no	—
98	(C₂×D₄₇)⋊C₄	—	2	8	no	—
99	C₄⋊Dic₄₇	—	2	1	no	—
100	C₄⋊Dic₄₇	C₄²	1	2	yes	—
101	C₄×Dic₄₇	—	2	1	no	—
102	C₄×Dic₄₇	—	2	1	no	—
103	C₄×Dic₄₇	—	2	1	no	—
104	C₄×Dic₄₇	—	2	1	no	—
105	C₄×Dic₄₇	—	4	2	no	—
106	C₄×Dic₄₇	—	4	4	no	—
107	C₄×Dic₄₇	C₂×C₈	1	4	yes	—
108	C₄×Dic₄₇	M₁₆	1	4	yes	—
109	C₂×C₄₇⋊C₈	—	2	2	no	—
110	C₂×C₄₇⋊C₈	—	2	2	no	—
111	C₂×C₄₇⋊C₈	—	4	2	no	—
112	C₂×C₄₇⋊C₈	—	4	1	no	—
113	C₂×C₄₇⋊C₈	—	4	1	no	—
114	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×D₄₇	—	2	2	no	—
116	C₂²×D₄₇	—	2	4	no	—
117	C₂²×D₄₇	—	4	1	no	—
118	C₂²×D₄₇	—	4	1	no	—
119	C₂²×D₄₇	—	4	2	no	—
120	C₂×C₄×C₄₇	—	2	2	no	—
121	C₂×C₄×C₄₇	—	2	4	no	—
122	C₂×C₄×C₄₇	—	4	2	no	—
123	C₂×C₄×C₄₇	—	4	2	no	—
124	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
125	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
126	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
127	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
128	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
129	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
130	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
131	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
132	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
133	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
134	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
135	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
136	C₂×Dic₄₇	—	2	2	no	—
137	C₂×Dic₄₇	—	2	2	no	—
138	C₂×Dic₄₇	—	2	2	no	—
139	C₂×Dic₄₇	—	2	2	no	—
140	C₂×Dic₄₇	—	2	2	no	—
141	C₂×Dic₄₇	—	4	1	no	—
142	C₂×Dic₄₇	—	4	1	no	—
143	C₂×Dic₄₇	C₂²⋊C₈	1	4	yes	—
144	C₂×Dic₄₇	C₂²⋊C₈	1	4	yes	—
145	D₁₈₈	—	2	2	no	—
146	D₁₈₈	—	2	4	no	—
147	D₁₈₈	C₄×C₈	1	4	yes	complemented
148	C₄×D₄₇	—	4	16	no	—
149	C₄×D₄₇	—	4	2	no	—
150	C₄×D₄₇	—	4	2	no	—
151	C₄×D₄₇	—	4	2	no	—
152	C₄×D₄₇	—	4	2	no	—
153	C₈×C₄₇	—	4	2	no	—
154	C₈×C₄₇	—	4	2	no	—
155	C₄₇⋊C₈	—	4	2	no	—
156	C₄₇⋊C₈	—	4	2	no	—
157	#8170	—	47	1	no	maximal, Sylow
158	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄₇	C₂×C₂²⋊C₈	1	2	yes	—
160	C₂²×C₄₇	#417	1	1	yes	characteristic
161	C₂²×C₄₇	#418	1	1	yes	characteristic
162	C₂²×C₄₇	#421	1	2	yes	—
163	C₂×D₄₇	—	2	4	no	—
164	C₂×D₄₇	—	4	4	no	—
165	C₂×D₄₇	—	4	4	no	—
166	C₂×D₄₇	—	4	2	no	—
167	C₂×D₄₇	—	4	2	no	—
168	C₄×C₄₇	—	2	1	no	—
169	C₄×C₄₇	—	2	1	no	—
170	C₄×C₄₇	—	4	4	no	—
171	C₄×C₄₇	C₂×C₄×C₈	1	1	yes	characteristic
172	C₄×C₄₇	C₄×M₁₆	1	1	yes	characteristic
173	C₄×C₄₇	#431	1	2	yes	—
174	C₄×C₄₇	#440	1	1	yes	characteristic
175	C₄×C₄₇	#440	1	1	yes	characteristic
176	C₄×C₄₇	#442	1	1	yes	characteristic
177	C₄×C₄₇	#442	1	1	yes	characteristic
178	Dic₄₇	—	2	4	no	—
179	Dic₄₇	—	2	4	no	—
180	Dic₄₇	—	4	2	no	—
181	C₄²×D₄	—	47	1	no	—
182	C₄×C₄⋊C₈	—	47	1	no	—
183	#1744	—	47	1	no	—
184	C₂×D₄⋊C₈	—	47	1	no	—
185	C₂×D₄⋊C₈	—	47	1	no	—
186	#1279	—	47	1	no	—
187	#1279	D₄₇	1	1	yes	characteristic, complemented
188	C₂×C₄₇	#1477	1	2	yes	—
189	C₂×C₄₇	#1478	1	2	yes	—
190	C₂×C₄₇	C₄×C₂²⋊C₈	1	1	yes	characteristic
191	C₂×C₄₇	#1759	1	1	yes	characteristic
192	C₂×C₄₇	#1762	1	1	yes	characteristic
193	D₄₇	—	4	4	no	—
194	C₂×C₄×D₄	—	47	2	no	—
195	C₂×C₄×D₄	—	47	1	no	—
196	C₂²×C₄²	—	94	1	no	—
197	C₂×C₄⋊C₈	—	47	1	no	—
198	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
199	C₂×C₄×C₈	—	47	1	no	—
200	C₂×C₄×C₈	—	94	1	no	—
201	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
202	C₄×C₄⋊C₄	—	47	2	no	—
203	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
204	C₄×C₂²⋊C₄	—	94	2	no	—
205	C₄×C₂²⋊C₄	—	94	1	no	—
206	C₄³	—	47	1	no	—
207	#336	—	94	2	no	—
208	#336	—	94	1	no	—
209	D₄⋊C₈	—	47	4	no	—
210	D₄⋊C₈	—	47	4	no	—
211	C₄₇	#8170	1	1	yes	characteristic, complemented, Sylow
212	C₂²×D₄	—	47	1	no	—
213	C₂³×C₄	—	94	2	no	—
214	C₂³×C₄	—	94	1	no	—
215	C₂²×C₈	—	2	1	no	—
216	C₂²×C₈	—	2	1	no	—
217	C₂²×C₈	—	94	1	no	—
218	C₂²×C₈	—	94	1	no	—
219	C₄×D₄	—	47	8	no	—
220	C₄×D₄	—	47	2	no	—
221	C₄×D₄	—	47	2	no	—
222	C₄×D₄	—	94	4	no	—
223	C₄×D₄	—	94	1	no	—
224	C₄×D₄	—	94	1	no	—
225	C₂×C₄⋊C₄	—	47	1	no	—
226	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
227	C₂×C₂²⋊C₄	—	94	2	no	—
228	C₂×C₂²⋊C₄	—	94	1	no	—
229	C₂×C₄²	—	2	1	no	—
230	C₂×C₄²	—	47	2	no	—
231	C₂×C₄²	—	47	1	no	—
232	C₂×C₄²	—	47	1	no	—
233	C₂×C₄²	—	47	2	no	—
234	C₂×C₄²	—	94	2	no	—
235	C₂×C₄²	—	188	2	no	—
236	C₂×C₄²	—	188	2	no	—
237	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
238	C₄⋊C₈	—	2	1	no	—
239	C₄⋊C₈	—	47	2	no	—
240	C₄⋊C₈	—	94	1	no	—
241	C₄⋊C₈	C₄×D₄₇	1	2	yes	complemented
242	C₄×C₈	—	2	1	no	—
243	C₄×C₈	—	47	2	no	—
244	C₄×C₈	—	94	1	no	—
245	C₄×C₈	—	188	2	no	—
246	C₄×C₈	C₄×D₄₇	1	2	yes	complemented
247	#95	—	2	1	no	—
248	#95	—	94	2	no	—
249	C₂⁴	—	94	1	no	—
250	C₂×D₄	—	47	2	no	—
251	C₂×D₄	—	47	4	no	—
252	C₂×D₄	—	94	1	no	—
253	C₂×D₄	—	94	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	47	2	no	—
256	C₂²×C₄	—	47	2	no	—
257	C₂²×C₄	—	94	8	no	—
258	C₂²×C₄	—	94	1	no	—
259	C₂²×C₄	—	94	2	no	—
260	C₂²×C₄	—	94	2	no	—
261	C₂²×C₄	—	188	4	no	—
262	C₂²×C₄	—	188	4	no	—
263	C₂²×C₄	—	188	1	no	—
264	C₂²×C₄	—	188	1	no	—
265	C₂²×C₄	—	188	1	no	—
266	C₂²×C₄	—	188	1	no	—
267	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
268	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
269	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	4	2	no	—
273	C₂×C₈	—	4	1	no	—
274	C₂×C₈	—	4	1	no	—
275	C₂×C₈	—	94	2	no	—
276	C₂×C₈	—	94	2	no	—
277	C₂×C₈	—	188	2	no	—
278	C₂×C₈	—	188	1	no	—
279	C₂×C₈	—	188	1	no	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	47	2	no	—
282	C₄⋊C₄	—	94	1	no	—
283	C₄⋊C₄	C₈×D₄₇	1	4	yes	—
284	C₂²⋊C₄	—	94	8	no	—
285	C₂²⋊C₄	—	94	2	no	—
286	C₂²⋊C₄	—	94	2	no	—
287	C₄²	—	4	1	no	—
288	C₄²	—	4	1	no	—
289	C₄²	—	47	4	no	—
290	C₄²	—	47	4	no	—
291	C₄²	—	94	1	no	—
292	C₄²	—	94	1	no	—
293	C₄²	—	94	1	no	—
294	C₄²	—	94	1	no	—
295	C₄²	—	188	2	no	—
296	C₄²	—	188	4	no	—
297	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
298	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
299	C₄²	#10625352	1	1	yes	characteristic
300	C₄²	#10625354	1	1	yes	characteristic
301	C₂³	—	94	2	no	—
302	C₂³	—	94	4	no	—
303	C₂³	—	188	1	no	—
304	C₂³	—	188	1	no	—
305	C₂³	—	188	2	no	—
306	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
307	D₄	—	47	4	no	—
308	D₄	—	94	2	no	—
309	D₄	—	94	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	47	4	no	—
315	C₂×C₄	—	47	4	no	—
316	C₂×C₄	—	94	2	no	—
317	C₂×C₄	—	94	2	no	—
318	C₂×C₄	—	94	2	no	—
319	C₂×C₄	—	94	2	no	—
320	C₂×C₄	—	94	2	no	—
321	C₂×C₄	—	188	16	no	—
322	C₂×C₄	—	188	1	no	—
323	C₂×C₄	—	188	1	no	—
324	C₂×C₄	—	188	2	no	—
325	C₂×C₄	—	188	2	no	—
326	C₂×C₄	—	188	2	no	—
327	C₂×C₄	—	188	2	no	—
328	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
329	C₂×C₄	#13093982	1	1	yes	characteristic
330	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
331	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
332	C₂×C₄	#13093986	1	1	yes	characteristic
333	C₂×C₄	#13093986	1	1	yes	characteristic
334	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
335	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
336	C₂×C₄	#13094048	1	1	yes	characteristic
337	C₂×C₄	#13094051	1	1	yes	characteristic
338	C₂×C₄	#13094051	1	1	yes	characteristic
339	C₂×C₄	#13094056	1	1	yes	characteristic
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₈	—	188	2	no	—
343	C₈	—	188	2	no	—
344	C₂²	—	94	4	no	—
345	C₂²	—	188	2	no	—
346	C₂²	—	188	4	no	—
347	C₂²	—	188	4	no	—
348	C₂²	—	188	2	no	—
349	C₂²	#15688970	1	1	yes	characteristic
350	C₂²	C₂²⋊C₈×D₄₇	1	2	yes	—
351	C₂²	#15689123	1	1	yes	characteristic
352	C₂²	#15689126	1	1	yes	characteristic
353	C₂²	#15689138	1	2	yes	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	4	4	no	—
357	C₄	—	94	4	no	—
358	C₄	—	94	4	no	—
359	C₄	—	188	2	no	—
360	C₄	C₄×C₈×D₄₇	1	1	yes	characteristic
361	C₄	#15689075	1	1	yes	characteristic
362	C₄	#15689175	1	2	yes	—
363	C₄	#15689222	1	1	yes	characteristic
364	C₄	#15689226	1	1	yes	characteristic
365	C₄	#15689232	1	1	yes	characteristic
366	C₄	#15689234	1	1	yes	characteristic
367	C₂	—	188	4	no	—
368	C₂	#20241774	1	2	yes	—
369	C₂	#20241777	1	2	yes	—
370	C₂	#20243145	1	1	yes	characteristic
371	C₂	#20243197	1	1	yes	characteristic
372	C₂	#20243212	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1279	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1279	D₄₇
hypocenter	C₄₇	#8170
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₄⋊C₈×Dic₄₇	C₂	semidirect
3. #20243133	C₂	semidirect
6. #20241229	C₂	semidirect
7. C₄₇×#1279	C₂	semidirect
20. #15688852	C₄	semidirect
21. #15688850	C₄	semidirect
35. #13093986	C₈	semidirect
47. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
49. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
58. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
60. C₄×C₈×C₄₇	C₂×C₄	semidirect
147. D₁₈₈	C₄×C₈	semidirect
187. #1279	D₄₇	semidirect
211. C₄₇	#8170	semidirect
241. C₄⋊C₈	C₄×D₄₇	semidirect
246. C₄×C₈	C₄×D₄₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×#13093986	2
C₄⋊C₈×Dic₄₇	2
#20243133	2
C₂×#15688852	2
C₂×#15688850	2
#20241229	2
C₄₇×#1279	2
#8170	47